im trying to write an algorithm concerning the HMM. My matlab knowledge is limited so im overwhelmed by most of the hmm-toolboxes.
In my example i've got a 4 state system with a known Transition Matrix(4x4). The state probabilities are unknown (hidden markov... d'uh!). To get the probabilities of each state (P1,P2,P3,P4), i declare the first state probability with "P1=1" and my last State "P4=0" and calculate the others through my transition matrix.
But at the end my state probabilites should sum up to: P1+P2+P3+P4= 1
(S1 and S4 are not connected)
The algorithm is about the failure/repair-rate of a machine. So each State has at least 2 incoming and 2 outgoing variables. My TransitionMatrix looks like this then: T= (a11 a12 a13 a14; a21 a22 a23 a24; a31 a32 a33 a34; a41 a42 a43 a44)
a11= -(a12+a13+a14); a22 = -( a21+ a23 +a24); a33= ... etc so that the sum of each row equals zero.
AS you can (not-)see i dont have any code yet, but i would really appreciate some help/hints, how to realise it. Thank You!